[guest39538]

Interestingly, it's what the police mostly talk about in road safety lectures. If Mr Plod understands it, and can somehow transfer that understanding to speeding teenage halfwits, it seems strange that anyone who contributes to this forum has a problem with it.

Oh please, I clearly understand it but like to dig deep for a deeper understanding, I have my answer, it is abstract and not really a physical thing involving energy.


Do falling objects regardless of their mass have the same terminal velocity?

[guest39538]

It may be abstract but it certainly isn't meaningless.

Well we could describe it mas, height, acceleration= d(x) it will travel

h*a=F

[hamdani yusuf]

Do falling objects regardless of their mass have the same terminal velocity?

No. Small rain drops have lower terminal velocity than bigger rain drops, even though they consist of the same material.
Terminal velocity of a falling object is achieved when down force by gravity equals up force by air resistance, hence it is affected by many factors, e.g. air pressure, temperature, humidity, and the object's density, form, orientation, size, etc.

[alancalverd]

I clearly understand it but like to dig deep for a deeper understanding

There's nothing deeper to understand. The kinetic energy of a mass m moving at velocity v is ½mv². It's a useful concept because (by experiment) energy is conserved in classical physics, so we can use it to predict what happens when our moving object interacts with something else.

[guest39538]

I clearly understand it but like to dig deep for a deeper understanding

There's nothing deeper to understand. The kinetic energy of a mass m moving at velocity v is ½mv². It's a useful concept because (by experiment) energy is conserved in classical physics, so we can use it to predict what happens when our moving object interacts with something else.

I am sure there is another present piece of maths that gives the exact same answer, something involving the equivalance principle.   Is it F=ma?

[jeffreyH]

Except that kinetic energy that is constant has no acceleration. Therefore there is zero force. As well as having stated F=ma, Newton also has a first law which precludes acceleration. You should look it up. It describes states with no forces acting on an object. So that an object at rest remains at rest and an object with constant speed carries on in a straight line with the same constant speed. Because NO FORCES ARE ACTING UPON THE OBJECT!

[guest39538]

Except that kinetic energy that is constant has no acceleration.

A piece of maths has no acceleration or velocity or anythng else for that matter because it is abstract.   I think you mean the object in motion will remain in motion unless acted upon by external forces.  An object in spacial motion away from an inertial reference frame, remains without force until it impacts another body  . A falling body that the force is redirected of, will continue in a parallel motion until the potential force disperses an dis lost to the external force of gravity.


→
p=F


p₀=Fn


var(p)=var(Fn)

Newtons third law ''the ground pushes back'',


It is positive energy that pushes back and is the resistance to compression.


 [ Invalid Attachment ]

[evan_au]

I am sure there is another present piece of maths that gives the exact same answer, something involving the equivalance principle.

This thread is discussing conservation of Energy (of which Kinetic Energy and Potential Energy are two forms), under the influence of a gravitational field.

Emmy Noether came up with a very general concept which links conservation laws to symmetries in nature.

The Conservation of Energy (and its component Kinetic Energy) is proved in the following example:
http://en.wikipedia.org/wiki/Noether%27s_theorem#Example_1:_Conservation_of_energy
 
Occasionally, conservation of momentum comes up in this thread - this is another principle which can be proved by Noether's theorem.

Do falling objects regardless of their mass have the same terminal velocity?

"raindrops falling through air to reach terminal velocity" is a complex system in which it is extremely hard to add up all the tiny contributions of kinetic energy which are distributed amongst all the individual air molecules. So if you wish to understand kinetic energy, look at objects falling in a vacuum (or the proverbial cannonballs falling from the leaning tower of Pisa) - it is so much easier to analyze.

You can see something real, without being diverted into fractal flurries of turbulence which dissipate lots of energy and get you nowhere.

p₀=F_n etc

The mathematical notation used in Noether's Theorem may look superficially similar to some equations previous posted in this thread. It is not.

[guest39538]

I am sure there is another present piece of maths that gives the exact same answer, something involving the equivalance principle.

This thread is discussing conservation of Energy (of which Kinetic Energy and Potential Energy are two forms), under the influence of a gravitational field.

Emmy Noether came up with a very general concept which links conservation laws to symmetries in nature.

The Conservation of Energy (and its component Kinetic Energy) is proved in the following example:
http://en.wikipedia.org/wiki/Noether%27s_theorem#Example_1:_Conservation_of_energy
 
Occasionally, conservation of momentum comes up in this thread - this is another principle which can be proved by Noether's theorem.

Do falling objects regardless of their mass have the same terminal velocity?

"raindrops falling through air to reach terminal velocity" is a complex system in which it is extremely hard to add up all the tiny contributions of kinetic energy which are distributed amongst all the individual air molecules. So if you wish to understand kinetic energy, look at objects falling in a vacuum (or the proverbial cannonballs falling from the leaning tower of Pisa) - it is so much easier to analyze.

You can see something real, without being diverted into fractal flurries of turbulence which dissipate lots of energy and get you nowhere.

p₀=F_n etc

The mathematical notation used in Noether's Theorem may look superficially similar to some equations previous posted in this thread. It is not.

That is new to me, I have no idea what it means yet. 

I had this thought though after looking at the link


Φ→← =  Φ←→  = 4/3 pi r³ 


>Φ→← = <4/3 pi r³

>Φ←→ = >4/3 pi r³


E=>Φ→←

[alancalverd]

I am sure there is another present piece of maths that gives the exact same answer, something involving the equivalance principle.   Is it F=ma?

Kind of.

Energy = work = force x distance = (mass x acceleration) x distance =  mass x ½(velocity change)², if you think about it.

Classical physics really is very simple. It's all about precise definitions of mathematical quantities, and finding the conservation laws that apply to them. And as I've said many times before, dimensional analysis will always resolve any mistakes or misunderstandings.